Algebra Examples

$\frac{2 y - 6 x}{3 x} = 2 y - 2$

Step 1

Multiply both sides by $3 x$ .

$\frac{2 y - 6 x}{3 x} (3 x) = (2 y - 2) (3 x)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2 y - 6 x}{3 x} (3 x)$ .

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Step 2.1.1.1

Rewrite using the commutative property of multiplication.

$3 \frac{2 y - 6 x}{3 x} x = (2 y - 2) (3 x)$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $3 x$ .

$3 \frac{2 y - 6 x}{3 (x)} x = (2 y - 2) (3 x)$

Step 2.1.1.2.2

Cancel the common factor.

$3 \frac{2 y - 6 x}{3 x} x = (2 y - 2) (3 x)$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{2 y - 6 x}{x} x = (2 y - 2) (3 x)$

Step 2.1.1.3

Cancel the common factor of $x$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{2 y - 6 x}{x} x = (2 y - 2) (3 x)$

Step 2.1.1.3.2

Rewrite the expression.

$2 y - 6 x = (2 y - 2) (3 x)$

Step 2.1.1.4

Reorder $2 y$ and $- 6 x$ .

$- 6 x + 2 y = (2 y - 2) (3 x)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(2 y - 2) (3 x)$ .

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Step 2.2.1.1

Apply the distributive property.

$- 6 x + 2 y = 2 y (3 x) - 2 (3 x)$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Rewrite using the commutative property of multiplication.

$- 6 x + 2 y = 2 \cdot 3 y x - 2 (3 x)$

Step 2.2.1.2.2

Multiply $3$ by $- 2$ .

$- 6 x + 2 y = 2 \cdot 3 y x - 6 x$

Step 2.2.1.2.3

Multiply $2$ by $3$ .

$- 6 x + 2 y = 6 y x - 6 x$

Step 2.2.1.2.4

Move $y$ .

$- 6 x + 2 y = 6 x y - 6 x$

Step 3

Solve for $y$ .

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Step 3.1

Subtract $6 x y$ from both sides of the equation.

$- 6 x + 2 y - 6 x y = - 6 x$

Step 3.2

Move all terms not containing $y$ to the right side of the equation.

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Step 3.2.1

Add $6 x$ to both sides of the equation.

$2 y - 6 x y = - 6 x + 6 x$

Step 3.2.2

Add $- 6 x$ and $6 x$ .

$2 y - 6 x y = 0$

Step 3.3

Factor $2 y$ out of $2 y - 6 x y$ .

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Step 3.3.1

Factor $2 y$ out of $2 y$ .

$2 y (1) - 6 x y = 0$

Step 3.3.2

Factor $2 y$ out of $- 6 x y$ .

$2 y (1) + 2 y (- 3 x) = 0$

Step 3.3.3

Factor $2 y$ out of $2 y (1) + 2 y (- 3 x)$ .

$2 y (1 - 3 x) = 0$

Step 3.4

Divide each term in $2 y (1 - 3 x) = 0$ by $2 (1 - 3 x)$ and simplify.

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Step 3.4.1

Divide each term in $2 y (1 - 3 x) = 0$ by $2 (1 - 3 x)$ .

$\frac{2 y (1 - 3 x)}{2 (1 - 3 x)} = \frac{0}{2 (1 - 3 x)}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $2$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{2 y (1 - 3 x)}{2 (1 - 3 x)} = \frac{0}{2 (1 - 3 x)}$

Step 3.4.2.1.2

Rewrite the expression.

$\frac{y (1 - 3 x)}{1 - 3 x} = \frac{0}{2 (1 - 3 x)}$

Step 3.4.2.2

Cancel the common factor of $1 - 3 x$ .

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Step 3.4.2.2.1

Cancel the common factor.

$\frac{y (1 - 3 x)}{1 - 3 x} = \frac{0}{2 (1 - 3 x)}$

Step 3.4.2.2.2

Divide $y$ by $1$ .

$y = \frac{0}{2 (1 - 3 x)}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Cancel the common factor of $0$ and $2$ .

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Step 3.4.3.1.1

Factor $2$ out of $0$ .

$y = \frac{2 (0)}{2 (1 - 3 x)}$

Step 3.4.3.1.2

Cancel the common factors.

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Step 3.4.3.1.2.1

Cancel the common factor.

$y = \frac{2 \cdot 0}{2 (1 - 3 x)}$

Step 3.4.3.1.2.2

Rewrite the expression.

$y = \frac{0}{1 - 3 x}$

Step 3.4.3.2

Divide $0$ by $1 - 3 x$ .

$y = 0$